Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Optimum positive linear schemes for advection in two and three dimensions
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
Residual Distribution Schemes for Conservation Laws via Adaptive Quadrature
SIAM Journal on Scientific Computing
Journal of Computational Physics
Anti-diffusive flux corrections for high order finite difference WENO schemes
Journal of Computational Physics
Essentially non-oscillatory Residual Distribution schemes for hyperbolic problems
Journal of Computational Physics
Recovering High-Order Accuracy in WENO Computations of Steady-State Hyperbolic Systems
Journal of Scientific Computing
Residual Distribution Schemes on Quadrilateral Meshes
Journal of Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems
Journal of Computational Physics
A first-order system approach for diffusion equation. I: Second-order residual-distribution schemes
Journal of Computational Physics
Incremental unknowns method based on the θ-scheme for time-dependent convection-diffusion equations
Mathematics and Computers in Simulation
Journal of Computational Physics
A first-order system approach for diffusion equation. II: Unification of advection and diffusion
Journal of Computational Physics
Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case
Journal of Computational Physics
High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
SIAM Journal on Scientific Computing
Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state hyperbolic conservation laws on non-smooth Cartesian or other structured curvilinear meshes. WENO (weighted essentially non-oscillatory) integration is used to compute the numerical fluxes based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. In two space dimension, the computational cost of our scheme is comparable to that of a high order WENO finite difference scheme and is therefore much lower than that of a high order WENO finite volume scheme, yet the new scheme does not have the restriction on mesh smoothness of the traditional high order conservative finite difference schemes. A Lax-Wendroff type theorem is proved for convergence towards weak solutions in one and two dimensions, and extensive numerical experiments are performed for one- and two-dimensional scalar problems and systems to demonstrate the quality of the new scheme, including high order accuracy on non-smooth meshes, conservation, and non-oscillatory properties for solutions with shocks and other discontinuities.